Methodology for strength distribution estimation of ceramics from ball-on-three-balls and four-point bending experiments, Weibull statistics and fractographic investigations: Application to magnesium aluminum spinel

Abstract

The present paper aims to propose a reliable analysis of ball-on-three-balls and four-point bending experiments applied to advanced ceramics combining statistical analyses, numerical modelling and fractography. MgAl2O4 transparent spinel ceramic was selected to facilitate the assessment of samples quality. Following the material processing procedure detailed in the literature, numerous spinel samples of two different geometries (20 and 60 mm in diameter) were produced. Knoop Hardness and Young's modulus values of 11.8 GPa and 290 GPa were measured, respectively. A three-modal grain size distribution was observed through the sample's thickness. Biaxial bending tests have been performed in conjunction with numerical simulations using Abaqus/Standard®. Thus, parallelism defects were taken into account and their effects on the maximal stress and effective volume were quantified. They were found to be very close to the only published data. In addition, four-point bending experiments were carried out and validated using an ultra-high-speed camera. The scattering of the bending strength was modelled using a two-parameter Weibull distribution and the maximum likelihood approach. 90% confidence intervals of the parameters and confidence bounds of the probability of failure were computed using the likelihood ratio test. This approach is more suitable than Monte Carlo simulations with regard to computational costs. According to the Weibull theory and biaxial bending strength distribution, the material strength, rescaled for different effective volumes was slightly overestimated, in comparison with four-point bending results. Fractographic analyses on uniaxial bending samples revealed that fractures originate from large grains. The corresponding study on biaxial bending samples revealed that carbon inclusions located near to the surface seem to be responsible for failure. Finally, this study brings additional arguments for a more intensive use of the ball-on-three-balls set-up especially when concerns about costs, sample geometry and test practicality are raised.